The vector is perpendicular to and parallel to

MATHEMATICS · Subjective · A Level · Mathematics · Vectors · Vectors

Problem

The vector

\vec{v}=3\mathbf{i}-\lambda\mathbf{j}+2\lambda\mathbf{k}

is perpendicular to

\vec{a}=\mathbf{i}+5\mathbf{j}+\mathbf{k}

and parallel to

\vec{b}=6\mathbf{i}-2\mathbf{j}+4\mathbf{k}

. Determine the value of

\lambda